Answer: r=√6 or r≈2.45.
Step-by-step explanation:
To find the radius, you first need to know the equation of a circle.
Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex]
Now that we know the equation of the circle, we can use it to find the radius of the given equation.
3.5(x+2.2)²+3.5(y-11.1)²-21=0
So far the equation looks pretty similar with the exception of the bolded areas. To get rid of them, we need to use our algebraic properties.
3.5(x+2.2)²+3.5(y-11.1)²-21=0 [add both sides by 21]
3.5(x+2.2)²+3.5(y-11.1)²=21 [factor out 3.5]
3.5((x+2.2)²+(y-11.1)²)=21 [divide both sides by 3.5]
(x+2.2)²+(y-11.1)²=6
Now, our equation is the same as the one posted above. You may think that 6 is our radius, but if you look closely, the equation is equal to r². Therefore, 6 is actually r², not r.
r²=6 [square root both sides]
r=√6
Finally, we have the final answer, r=√6 or r≈2.45.
